Intramolecular interactions in rhodium monoxide and halogen azides

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I

n t r a m o l e c u l a r

I

n t e r a c t i o n s

IN

R

h o d i u m

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o n o x i d e

a n d

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a l o g e n

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z i d e s

by

Roy Henry Jensen

B.Sc., U niversity o f V ictoria, 1995 M .Sc., U niversity o f D enver, 1999

A dissertation subm itted in partial fulfillm ent o f the requirem ent for the degree o f

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o c t o r o f

P

h il o so ph y

in the D epartm ent o f Chemistry.

W e accept this dissertation as conform ing to the required standard.

ter B alfour, Sup

Dr. W alter B alfour, Supervisor Department o f Chemistry, U n iv ersitj^ f Victoria

rolo. C om m ittee M em ber istry. University o f Victoria

Dr. D avid H arrington, Com m ittee M em ber Department o f Chemistry, University o f Victoria

Dr. Terry Department o f

m ittee M em ber , University ofV ietoria

Dr. Jerem y Tatum, Com m ittee M em ber Department o f Physics and Astronomy, University ofV ietoria

f, E xA h

Dr. M ichael Gepfy, Ejatlm al Exam iner Department o f Chemistry, University o f British Columbia

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A

b s t r a c t

Supervisor: Dr. W alter B alfour

Part

A. V ibronic transitions o f rhodium m onoxide (R h '^ 0 and Rh^^O) w ere observed in the 380 to 700 nm region. Laser-induced fluorescence identified tw o ^fl^ - X ‘^IT progres sions w ith origins at {15 667, 15 976} and {15 874, 16 167} cm"'. These progressions

w ere labeled [15.8] and [16.0] ^fl - X^TT, respectively. V ibrational param eters

w ere determ ined for the ground and excited states; the ground state param eters are a>e = 805.4 ± 0.6 c m '\ (OsXe - 4.5 ± 0.1 cm'*, and De = 35 800 ± 800 cm'*. Evidence w as found for low -lying electronic states at 3 747, 5 980 and 6 475 cm *. Lifetim e m easure

m ents are consistent w ith the spin-forbidden nature o f the transition: ^ lï - "*S“.

Part B.

D ensity functional and configuration interaction calculations on the low est singlet and triplet potential energy surfaces o f hydrogen, fluorine, and chlorine azide for the

reactions X N ^ iX * A ') NX(X^Z; a*A) + N2(X*Eg) and A N s ► X (X ^S; X^Pg/z) +

N3(X^rig) (X = H, F, Cl) show that the low est energy dissociation pathw ay proceeds exo-

therm ically to NA(a) + N2. This surface is crossed on the bound singlet region by a disso

ciative triplet surface. U nim olecular decom position rates for each pathw ay and the

branching ratio support the experim ental observations: H N3 dissociates to ground state

products w hile FN3 and CIN3 produce significant am ounts o f electronically excited NA.

Dr. W alter Balfour, Supervisor Department o f Chemistn', University ofV ietoria

re Brolo, C om m ittee M em ber

hemistry. U niversity o fV ie to ria

Dr. D avid H arrington, C om m ittee M em ber Department o f Chemistry, University ofV ietoria

Dr. Terry Gcm ggJCom m ittee M em ber Department o f Chemistry, University ofV ietoria

Dr. Jerëm y Tatum , Com m ittee M em ber

D epartm ent o f Physics and Astronom y, U niversity o fV ie to ria

Dr. M ichael GeA-y, Exrem al Exam iner Department o f Chemistry, University o f British Columbia

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o n t e n t s Ab s t r a c t iii Ta b l e o f Co n t e n t s iv Lis t o f Ta b l e s viii Lis t o f Fig u r e s xi Ep ig r a p h xiv Pa r t A : Vi b r o n ic An a l y s is o f Rh o d iu m Mo n o x id e i 1. In t r o d u c t i o n 2 2. Q u a n t u m M e c h a n i c s OF V i b r o n i c T r a n s i t i o n s 5

Potential energy curves 8

Energy levels 11

Vibrational transitions 12

Effect of isotope substitution on vibrational energy levels 14

V ibronic transitions 15

Electronic transitions 16

Electric moments 17

Electric dipole transitions 18

Excited state lifetimes 19

Lifetime determination 2 0

3. Ex p e r i m e n t a l Se t u p 2 2

Experimental components 2 2

Pulsed molecular beam source 2 2

Laser ablation assembly 2 4

Detection & data collection 2 5

Experimental details 2 6

Laser-induced fluorescence 2 6

Dispersed fluorescence 2 9

Excited state lifetimes 2 9

4. R e s u l t s AND D i s c u s s i o n 3 0

Laser-induced fluorescence experiments 3 0

Dispersed fluorescence experiments 36

Calculation o f spectroscopic constants 4 3

Excited state lifetimes 4 6

Summary 4 7

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Ap p e n d i x A : De f i n i t io n s, Ac r o n y m s, a n d Ab b r e v ia t i o n s 5 2

Ap p e n d i x B : Co l l e c t io n Op t ic s 53

Ap p e n d i x C : Dy e La s e r Ca l i b r a t i o n 5 5

Optogalvanic spectroscopy 55

Experiment & results 56

Summary 63 Ap p e n d i x D : Ty p i c a l In s t r u m e n t Se t t in g s 6 4 Pa r t B : Th e r m a l Dis s o c i a t io n o f Ha l o g e n Az id e s 65 1. In t r o d u c t i o n 6 6 Current understanding of HN3 69 Electronic states of HN3 71 [H,N,C,0] analogs of HN3 73

Current understanding o f FN3 and CIN3 75

Related halogen azides 76

2. Co m p u t a t i o n a l Ch e m is t r y 78

Wavefunctions, orbitals, and electronic configurations 80

Basis sets 82

Computational methods 8 8

Hartree-Fock method 8 8

Configuration interaction 93

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Part A: Vibronic Analysis of Rhodium Monoxide

Table 4.1 Band centers and assignment o f the vibronic transitions in RhO from

500 to 650 nm. All values reported in air. 35

Table 4.2 Reported bond lengths for the ground and [15.8] ^fl and [16.0] ^11

states o f RhO. From Reference 25. 36

Table 4.3 DF shifts from the pump laser energy, (a) the average o f all the DF transitions assigned to the specified transition; (b) if replicate spectra were recorded at a given excitation laser wavelength, the average is reported; (c) average does not include the band observed in 598.1 nm pumped DF spectrum; (d) transitions from X'*E"(u=l); (e) coincidental transitions from both X‘^E“(r>=0) and X'*2'(r»=l) (the higher energy transition is from v" = 1); and (f) this transition is not

assigned to the ^fl progressions investigated herein.

Table 4.4 Vibrational parameters for the [15.8] ^11 and [16.0] ^FI states o f RhO. (a) Reference 25.

Table 4.5 Calculated and experimental spectroscopic Rh^^O/Rh'^0 shifts o f the ^ n (i/=0,l,2) band positions.

Table 4.6 Band-averaged lifetimes o f the ^FI vibronic states taken at three to five unperturbed locations within the band. The uncertainty is ± 1 0 0

ns.

Table 4.7 Vibrational parameters for the X^ZT and the [15.8] and [16.0] states o f RhO. Ground state parameters from DF experiments; excited state parameters from LIF experiments.

Table C .l Observed optogalvanic transitions between 490 and 650 nm. Units of a: nanometers, andb: arbitrary.

40 43 44 46 48 59

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Part B: Thermal Dissociation of Halogen Azides

Table 1.1 Isomers, geometries, and relative energies o f [H,N,C,0] isomers. All molecules adopt a trans-bent geometry with a dihedral angle o f 180°. Bond lengths are in angstroms (± 0.01 Â) and angles in degrees (± 2°). (Uncertainties represent the range o f different experimental and

theoretical methods.) Methods for (a) B3LYP/6-31 lG(d,p)

(References 41 and 45), (b) QClSD/6-31 lG(d,p) (Reference 45), and

(c) MRD-Cl/6-31G(d,p)//UHF/6-31G(d,p) (Reference 44). 74

Table 2.1 Ab initio methods (standard methods) used in this dissertation. 103

Tahle 3.1 Ah initio and experimental geometry and energy of HN3 in the

ground state, singlet-triplet crossing, and o f the dissociation products. Bond lengths in angstroms, bond angles in degrees, and energies in c m '\ (a) Energies are scaled to make the energy o f the optimized ground state geometry zero. Zpe corrections are not included, (b) Reference 97. The values in bold are fixed during the

optimization. 1 1 0

Table 3.2 Ab initio and experimental geometry and energy o f FN3 in the

ground state, singlet-triplet crossing, dissociation maximum, and of

the dissociation products. Legend same as Table 3.1. I l l

Table 3.3 Ab initio and experimental geometry and energy o f CIN3 in the

ground state, singlet-triplet crossing, dissociation maximum, and of

the dissociation products. Legend same as Table 3.1. 112

Table 3.4 Ab initio (unsealed) and experimental vibrational energies (in cm'*) of HN3 in the ground state and at the singlet-triplet crossing, (a)

Reference 97. Zpes are scaled hy the factors in Table 3.8. 113

Table 3.5 Ab initio (unsealed) and experimental vibrational energies (in cm"') o f FN3 in the ground state, singlet-triplet crossing, and dissociation maximum, (a) Reference 97. Zpes are scaled by the factors in Table

3.8. 114

Table 3.6 Ab initio (unsealed) and experimental vibrational energies (in cm"') of CIN3 in the ground state, singlet-triplet crossing, and dissociation

maximum, (a) Reference 97. Zpes are scaled by the factors in Table

3.8. 114

Table 3.7 Ab initio (unsealed) and experimental vibrational energies o f singlet and triplet NH, NF, and NCI, and o f N2. (a) Experimental values

taken as <Ue - 2 co^e from Reference 97. 115

Table 3.8 Ab initio scaling factors calculated from AN3 and the dissociation

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Table 3.9 Summary o f energy partitioning during the dissociation of^YNs. 120

Table 4.1 Extrapolated CBS energy o f the ground state, singlet-triplet crossing,

singlet dissociation maximum, and dissociation products o f ÆN3

using the QCISD standard methods. Energies in hartrees.

Table 4.2 for Reactions (71) to (74) o f ZN3 with the QCISD standard

methods. The 6-311++G(3df,3pd) and CBS energies use the zpe from the 6-311++G(d,p) calculation, (a) the singlet zpe was used for the

(b) Reference 101; (c) Reference 102; (d) Reference 103.

Table 4.3 for Reactions (75) to (78) o f AN3 with the QCISD standard

methods. The 6-311++G(3df,3pd) and CBS energies use the zpe from the 6-311++G(d,p) calculation.

123

130

133

Table 4.4 Experimental A^Tf^gg and ab initio o f the species listed in

Reactions (84) to (87) at the QCISD/6-31++G(d,p) and QCISD/6-311 ++G(d,p) levels o f theory.

Table 4.5 Reactions (84) to (87) at the QCISD/6-31++G(d,p)

and QCISD/6-311++G(d,p) levels of theory.

Table 4.6 Intersystem crossing probabilities for AN3. (a) Experimental values;

(b) Reference 101; (c) Reference 102; (d) Reference 103.

Table D .l Geometry o f HN3 in the singlet and triplet states at the singlet-triplet crossing and the mean geometry for single-point calculations. The values in bold are fixed during the optimization.

Table D.2 Geometry o f FN3 in the singlet and triplet states at the singlet-triplet crossing and the mean geometry for single-point calculations. The values in bold are fixed during the optimization.

Table D.3 Geometry o f CIN3 in the singlet and triplet states at the singlet-triplet crossing and the mean geometry for single-point calculations. The values in bold are fixed during the optimization.

Table D.4 Vibrational energies o f the singlet and triplet spin-states o f AN3 at the

singlet-triplet crossing. 136 137 140 174 175 175 176

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Part A: Vibronic Analysis of Rhodium Monoxide

Figure 2.1 Typical diatomic potential energy curve, F(r), and superimposed

vibrational levels. 8

Figure 3.1 Experimental setup for collection o f LIF and DF. The optogalvanic

calibration experiment is discussed on page 61. 23

Figure 3.2 Timing signals for the computer timing card. Time zero is the left vertical dashed line with time increasing to the right. The right vertical dashed line corresponds to the rising edge o f the timing pulse sent to the digital delay generator (see Figure 3.3). The delay, duration, and pulse direction are indicated. All voltage pulses are 5 V. Some timing signals were not used in the experiments but are

included for completeness. 27

Figure 3.3 Timing signals for the digital delay generator. The left vertical dashed line is time zero supplied by the computer timing card (see Figure 3.2). The delay, duration, magnitude, and pulse direction are

indicated. 28

Figure 4.1 LIF spectrum o f RhO from 350 to 700 nm in 50 nm sections (a-g). The signal intensity is convoluted by the dye laser power and the detector sensitivity; signal to noise is a better measure of the relative intensity o f the transitions. The vertical scale o f (a), (b), (c), and (g)

are 2x magnified. 34

Figure 4.2 DF spectra o f the four vibrational progressions ^fl - X"*I“(y=0) (a-d) and - X"*! (i/=l) (e). Each spectrum is normalized to the same maximum intensity (the signal/noise ratio gives an indication o f the original intensity). The arrows identify reproducible features that are

not part o f the X'^Z” progressions (see text). 39

Figure 4.3 Energy level diagram o f the observed transitions. Vertical bars

cover 50 cm'^ (» 2 nm). ♦ are the expected band positions based on

fitting the observed transitions to co^(i' + )4 )- (W.x, (v + X f ■ 45

F ig u r e 4 .4 T y p ic a l lif e tim e p r o file (b lu e ) an d s in g le -e x p o n e n tia l fit (re d ) fo r a

rovibronic transition of RhO. 47

Figure 4.5 Potential curves and observed vibrational energy levels o f the ground

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levels are shown in the bottom inset; their absolute positions are

uncertain and are separated in the inset for convenience. 48

Figure B .l Original (a) and current (b) optical arrangement. The dashed lines indicate the focal point o f the lens or the acceptance angle o f the monochromator. The wavy lines indicate the extrema o f emission

collectable by the lens. (To scale.) 53

Figure B.2 Updated optical arrangement for spectroscopic data collection.

Legend same as Figure B .l. (To scale.) 54

Figure C .l Electrical circuit for optogalvanic measurements from a hollow

cathode lamp. 56

Figure C.2 Typical optogalvanic signal. 57

Figure C.3 Typical optogalvanic spectrum. The asterisks indicate unassigned

transitions. One o f several doublets is shown at 507.57 nm. 58

Figure C.4 Results o f OGE calibration. In (a), the observed OGE lines and signal intensity are plotted with the mirror presenting the lines that could be assigned to known atomic iron or neon transitions (Reference c). (b) presents the residuals for the calibration and the two trend lines in the

residuals (see text). 62

Part B: Thermal Dissociation of Halogen Azides

Figure 1.1 Lewis structures for (a) ionic and (b) covalent bonding o f azides. 6 8

Figure 1.2 Lewis structure ofÆN;. 69

Figure 2.1 Comparison o f the (a) hydrogenlike, (b) Slater, and (c) CGTFs atomic orbitals o f carbon. Vertical and horizontal scales are the same, however the « = 2 functions in (c) are sealed 3x. ( 1 Bohr = 0.529177

A)

87

Figure 2.2 Lewis structures and formal charges o f ozone. 93

Figure 3.1 Notation used for bond lengths and angles in ANg. 105

Figure 3.2 Relaxed potential energy curves (PECs) for dissociation ofVNg along the singlet (solid) and triplet (dashed) VN-NN pathways at the

UB3LYP/6-31++G(d,p) ( --- ) and UQCISD/6-31++G(d,p)

( --- ) levels o f theory. Inset: magnification o f the singlet-triplet crossing region at the UQCISD/6-31++G(d,p) ( ♦ ) and UQCISD/

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6-311++G(d,p) (■) levels of theory. Shading scheme; (a) HN3; (b)

F N3; (c) CIN3. 108

Figure 3.3 Relaxed PECs for dissociation o f ZN3 along the X -NN N pathway

(Reactions (3)) at the UB3LYP/6-31++G(d,p) ( --- ) and UQCISD/6- 31++G(d,p) ( ---) levels o f theory. Shading scheme:

H N3, F N3, CIN3. 109

Figure 3.4 Optimized X-N« and bond lengths during YN3 dissociation

along the singlet (solid) and triplet (dashed) Y N-NN pathways (Reactions (1) and (2)) at the UQClSD/6-31++G(d,p) ( ---) levels o f theory. Shading scheme: HN3, FN3, CIN3. The vertical dashed line

is the approximate equilibrium N a-N ^ bond length. 117

Figure 3.5 Optimized (a) X -N ^-N ^ and (b) N ^-N ^N ^ bond angles during XN3

dissociation along the X 4 -N N pathway. Legend same as Figure 3.4. 118

Figure 4.1 Extrapolated CBS energy for ground state HN3. 122

Figure 4.2 Unimolecular dissociation rates o f XN3 for the singlet (solid) and

triplet (dashed) XN-NN pathways (Reactions (1) and (2)) at the

UQCISD CBS energies. The average ( ) and max/min

( --- ) transition probabilities (Table 4.6) are plotted for the triplet

pathway. Shading scheme: HN3, FN3, CINj. 143

Figure 4.3 Lifetime ofX N3 from the QCISD CBS energies. The vertical dashed

line corresponds to 300 K. Legend same as Figure 4.2. 144

Figure 4.4 Branching ratio (solid) and lifetime (dashed) o f (a) NH(a) and (b)

NF(a) and NCl(a) ofX N3 based on the QCISD CBS energies. Legend

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The only limits in life

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In chemical compounds, bonding is envisioned as the overlap o f atomic orbitals to form molecular orbitals, into which electrons arrange themselves to minimize the total energy o f the system. I f the resulting energy is lower than the summed energy o f the isolated atoms, a bond forms and the system is stable.* The nature of chemical bonding has been the subject of extensive study — all o f chemistry, in fact. Diatomic compounds provide the simplest system in which to probe the interaction o f atoms. From a detailed under standing o f diatomic interactions, we gain the tools necessary to understand bonding and reactions in larger systems; combustion, catalysis, polymerization, protein folding, and biological replication are but a few broad areas of chemical interest.

Multiple techniques are available to probe intramolecular interactions. Spectroscopy — the interaction o f a molecule with electromagnetic radiation — has proved to be the most sensitive and the most versatile. Because of each compound’s unique spectroscopic sig nature, spectroscopy has been used to identify and characterize both known and unknown species. The varying energy across the electromagnetic spectrum probes different intramolecular processes. The valence electrons — those responsible for bonding — are probed by infrared (IR), visible, and ultraviolet (UV) radiation. IR radiation probes rovibrational levels while visible and UV (UV/Vis) radiation probes rovibronic levels. Emis sion spectroscopy is a more sensitive technique, more selective, and provides more infor mation on the system than absorption spectroscopy.

In addition to providing information on intramolecular interactions, knowledge o f known systems has allowed scientists to identify them in other environments. Scientists have been able to identify many features in the solar spectrum. Solar absorption lines have been assigned to over 60 elements and dozens o f molecules and molecular ions. For example, H2, OH, C2, CN, CO, MgH, and SiC have been observed in the photosphere and many

others — HP, HCl, H2O, FeH, CrH, AlCI, MgCN,^ and MgNC^ — in cooler sunspots.^

Their presence in such environments attests to the strong intramolecular bonding in these

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compounds. Notably, many o f these species involve bonds to transition metals. Many absorption features still elude assignment, making future spectroscopic studies o f small molecules relevant to the understanding o f solar and astrophysical processes. Back on Earth, our atmosphere is predominantly composed o f small molecules exposed to solar radiation. Solar photolysis plays an integral part in the chemical composition o f the atmosphere at all levels. Apart from life itself, solar irradiation is responsible for ground level smog, stratospheric ozone formation and depletion, and the ionosphere, to name a few. Spectroscopic techniques have been developed to simultaneously determine the local, gradient, and total column concentration of analytes in the atmosphere"^ and even a non-invasive method o f measuring the combustion efficiency o f an automobile engine in real time.^

Our laboratory has spectroscopically characterized many first- and second-row transition metal containing compounds. Since 1990, this has included TiCr,® VN,^ CrN,* MnH,^ FeH,“’ FeC,“ Y H ,‘^ YC,^^ YNH,^" Y 0 ,‘^ InO,*^ InO^^’ InCl and InCr,^^ and ReN.‘® We recently chose to investigate rhodium compounds since they have received little attention from the spectroscopic community but have become very important in industry. Rhodium- containing compounds are known to catalyze polymerization reactions, nitric acid synthe sis, hydrocarbon reformulation, ethanol production, and NO^; conversion in automobile catalytic converters, to name a few.^*’ RhH,^’ RhC,^^ and RhN^^ have been studied and characterized in this laboratory. RhO is the subject o f this dissertation and spectra o f RhF and RhS have been collected.

Rhodium monoxide (RhO) is one of the least well characterized o f the transition metal monoxides. Originally observed in 1968 by Lagerqvist and Scullman, the high-temperature emission spectrum was too congested to analyze.^"* In our experiments, a low-temperature emission spectrum was obtained using a supersonically cooled RhO generated in a Rh/Oz/He plasma. A complex array o f vibronic bands in the 380 to 700 nm region was recorded by laser-induced fluorescence (LIF). Except for highly congested band centers, these bands were rotationally resolved. Isotopic substitution experiments identified four bands between 615 and 640 nm with near-zero isotopic shift. These bands are proposed to

he i/ = 0 ^ v" = 0 (0-0) transitions and rotational analysis in our laboratory has identified

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[15.8] H - X V and [16.0] - x V with origins at {15 667, 15 976} and (15 874, 16 167} c m '\ respectively.^^ This dissertation focuses on the vibrational progressions

from these origins. isotopic substitution, laser-induced fluorescence spectroscopy,

dispersed fluorescence spectroscopy, and excited state lifetime measurements were made to characterize these bands and obtain information on the electronic states involved.

Previously, Citra and Andrews examined the infrared absorption spectra o f laser-ablated rhodium atoms co-deposited with oxygen in argon at 7 K and assigned vibrational fea tures at 799.0 and 759.8 cm ' to R h'^0 and R h'^0, respectively.^® Chen and Armentrout used thermodynamic data to estimate the R h -0 ground state bond dissociation energy. Do, at 33 800 cm"'.^^ Anion photoelectron spectroscopy identified the ground state and elec tronic energy levels at « 1 600, 3 800, 5 700 and 8 100 cm"'.^^ These electronic states

were assigned based on theoretical arguments as X^Zî/2, A^Z“, B^ri3/2, and

The vibrational intervals o f the ground and ^1 1 3 / 2 states were estimated at 730 ± 80 cm"'

and 800 ± 90 cm"', respectively. The present work improves upon the precision o f these assignments and, in some cases, suggests alternate assignments.

Theoretical analysis o f transition metal containing complexes is difficult owing to the high density o f low-lying electronic states and approximate consideration o f electron cor relation, relativity, spin-orbit coupling, spin-spin coupling, etc.^^ Small changes in basis set or computational method often have large effects on the resulting ordering o f states because o f the non-linear nature o f the calculations. Additionally, multiple unpaired elec trons, degenerate levels, and quantum mechanical approximations necessary to make the calculations tractable often lead to inaccuracies. Calculations on FeH^° and RhN^' exem plify the problems. Nevertheless, ab initio calculations often provide qualitative informa tion useful in understanding molecular spectra. Several groups predict the ground state of RhO to be 42-/6,32,33

It is important to note that the demands o f ab initio calculations on diatomic molecules are considerably higher than polyatomic molecules: the ability to obtain vibronically accurate potential energy surfaces for even a triatomic molecule is currently impossible, yet expected for diatomics.

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As the smallest molecular entity, diatomic compounds have received the most attention from both a theoretical and experimental perspective. From this history, several mathe matical models for diatomic molecules have evolved.

Apart from the acceptance o f the postulates o f quantum mechanics and the separability of the wavefunction into space and time components, one underlying assumption is regularly made in quantum mechanical studies; the Bom-Oppenheimer approximation.'*® This approximation supposes that the large mass difference between electrons and nuclei allows for the separation o f the motions o f the electrons and nuclei. The smallest ratio is for hydrogen where the mass ratio is 1:1 836. Thus, classically, electrons move at least 43 times faster than the nucleus ( V l8 3 6 ), allowing the electrons to find their optimum elec tronic configuration in the potential generated by near-stationary nuclei. In a wave- mechanics perspective, electrons are delocalized and nuclei do not oscillate. In this per spective, the Bom-Oppenheimer approximation results from the different rate at which the electrons and nuclei react to an external force on the system. The electronic redistribution is complete before the nuclei begin to react to the force and ‘instantly’ redistribute for every nuclear configuration. This separates the total wavefunction, % into electronic and nuclear terms: %ec and ÿ^uc- These terms can be separated further. Moving to the center-

of-mass reference frame separates the translational wavefunction, o f from the

remaining terms. In the absence o f an external field, the translating molecule can be con sidered as a free particle and has non-discrete (continuous) energy levels. The radial and

angular portions of are separable into vibrational and rotational wavefunctions, y/^

and y/r, respectively.^ Nuclear spin {y/\) and electron spin ((%) appear as a result o f rela- tivistic quantum mechanics and have no classical counterpart. What remains is the elec tronic wavefunction, y/^. The final separated wavefunction takes the form

* References 34 to 39 were used to prepare tfiis Chapter; individual citations are omitted. Other sources are cited as required.

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^ - ^ e le c ^ n u c *^elec “

For molecules without a center of inversion, the nuclear spin weighting is the same for each energy level* — y/[ will not be discussed further. Relativistic quantum mechanics

requires that the total wavefunction, be symmetric with respect to exchange of any two

bosons and antisymmetric with respect to exchange o f any two fermions (electrons)."" The vibrational wavefunction alternates even/odd symmetry with increasing vibrational quan

tum number, V.

For an isolated molecule, conservation laws demand that the total energy and total angular momentum remain unchanged. The distribution o f the total energy into kinetic and poten tial components can vary (as can the total angular momentum). Hamiltonian mathematics is used to evaluate this energy distribution problem. A potential field exists within every molecule by virtue of the charge on and position of the nuclei and electrons. Equation (2)

shows the Hamiltonian, for a multinuclear, multielectron system that contains kinetic,

T , and potential, V , energy operators for the electrons and nuclei.^ Other terms can be added to treat other interactions, such as spin-orbit coupling, spin-spin coupling, and interactions with external fields.

f, 2 j ^ ^ 4jT£'g ^ 47t£'g ^ w>a4 6'g

The energy o f the system is determined by solving the Schrodinger equation, (3).

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* The num ber o f nuclear spin states plays an important role in the spectroscopic study o f molecules possessing a center o f inversion. The nuclei are now indistinguishable and y/i m ust be considered. The intensity o f rovibronic transitions depend on the number o f nuclear symmetric, ( / + 1)(27 + 1), and antisymmetric, 7(2/ + 1), states and the number that are populated: all if the nuclei are fermions and one [symmetric state] if they are bosons.

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For fixed nuclear coordinates, the Bom-Oppenheimer approximation simplifies (2) to the electronic Hamiltonian

Solving the Schrodinger equation using the electronic Hamiltonian provides the electronic energy o f the system at that nuclear configuration. The total energy is obtained by including the Hamiltonian for nuclear potential energy (5), which is a constant under the Bom-Oppenheimer approximation. The total energy defines a classical 'turning point’ — the location where the kinetic energy is zero, wholly in its potential component. Repeating the calculation while iterating the nuclear coordinates generates a potential energy surface (PES), F(r).

Solution o f the Schrodinger equation using the nuclear kinetic Hamiltonian, (6), in the

potential V (t) provides the rotational and vibrational energy levels o f the system.

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Potential energy curves

For a diatomic molecule, a one dimensional ‘surface’ or curve (PEC) is generated. Experimen tally and computationally, the PEC adopts the profile shown in Eigure 2.1. At short intemuclear distances, intemuclear repulsion dominates and forces the nuclei apart. At long distances, there are no intemuclear interactions and the energy is the simple sum of the energy o f the isolated atoms.

At intermediate distances, dynamic electron-electron interactions serve to lower the total energy, resulting in a molecular bond.

Several mathematical formulae have been used to approximate PECs. Some functions, when sub stituted into (6), return analytical solutions for the rotational and vibrational

energy levels o f the system.

A Taylor series expansion o f the potential energy, F(r), about re leads to Intemuclear Distance (r)

Figure 2.1 Typical diatomic potential energy curve, V(r), and superimposed vibrational levels.

2! 3! (7)

The second term is zero. Setting E(oo) = 0 gives V(r^ = -De, the dissociation energy from the bottom o f the PES; this is often called the Dunham potential function:

= + ^ { r - r j + ~ { r - r j + ^ { r - r j + . . . ₍₈₎

(23)

Although accurate if taken to infinite order,* the Dunham equation cannot be solved ana lytically when substituted into (6). Approximate solutions were derived by Dunham and

form a basis for interpreting high-resolution spectra. The expression for the rotational and vibrational energy is given by

+ 1)]"

(9)

I m

Truncating (8) at the second term results in a parabola centered about re, which is the har

monic oscillator approximation.

= ( 10)

2!

Solving the Schrodinger equation for the harmonic oscillator results in equally spaced energy levels with spacing a>e, in c m '\ a>e is related to k via the reduced mass,^ ju.

G » °(k )= © .(k + K) (1 1)

The harmonic approximation is, at best, qualitatively correct near r^ and not suitable for analyzing vibrational progressions. It fails to predict the highly repulsive nature o f the PEC at short intemuclear separation, fails to account for dissociation at large intemuclear separation, and fails to account for the decreasing vibrational energy level spacing and finite number o f vibrational levels.

The Morse function, (13), is a widely used analytical function that accounts for several failings o f the harmonic oscillator potential."*^ The Morse funetion has three adjustable parameters; a harmonic vibrational constant, %, anharmonic vibrational constant, m©Xe,

* Assuming no interaction between electronic states.

(24)

and dissociation energy, D^. These variables are related through (14) and (15), resulting in two independent variables.

F “ or^^(r) = i)J l- e '^ ('" ''') f (13)

(.4)

If all three parameters have been experimentally determined, the system is overdeter mined in this theory. Comparison of the theoretical and experimentally derived parame ters can be informative as to the reasonableness o f the Morse function. For example, a comparison o f coqX.^ provides information on the goodness-of-fit in the anharmonic region — a region o f spectroscopic interest.

Solving the Schrodinger equation for the Morse potential results in an expression, (16), that accounts for the decreasing spacing between energy levels with increasing v and the finite number o f vibrational energy levels.

G " " - ( t / ) ( u + ai.jc. (t/ + x y (16)

This energy expression becomes increasingly inaccurate as the dissoeiation energy is approached. Extensions o f the Morse potential have been developed but have not found general acceptance.

It is unrealistic to believe that a classical function with few variables could represent a quantum mechanical system to infinite accuracy. All of the analytical potentials described above ‘work’ for the system of interest if the intramolecular forces they consider domi nate and all other forces are negligible. All become increasingly inaccurate with increas ing V and as the desired accuracy increases.

Alternatively, a numerical potential can be constructed from spectroscopically determined

(25)

(RKR) method, which determines the classical turning points o f the PEC from the spec troscopic data. The resulting PEC is spectroscopically accurate for determining energy level positions and transition intensities. Further, this method intrinsically takes into account interactions between electronic states that perturb the rovibrational levels.

Energy levels

Within the assumption that the wavefunction is separable, (1), there exist expressions for the energy states o f the translational, rotational, vibrational, and electronic wavefunctions. Despite this separation, rotational constants do depend on the vibrational and electronic state in which they are found and vibrational constants do depend on their electronic state. Under the assumption o f separability, there is no intramolecular conversion from one form to another without the influence of an outside force, such as collisions or photons.

The closeness o f the translational energy levels means that a continuum o f speeds is observed, not discrete levels. The distribution depends on the experimental conditions.

The expression for the rotational energy levels within a given vibrational state is given by

where J is the rotational quantum number and Bv, Dv, etc., are rotational constants for a given vibrational level. In practice, experimental uncertainty and a limited number of observable rotational levels often prevents statistical determination o f values beyond Dv, sometimes only at Bv. Analytical expressions for the rotational constants can be obtained for some o f the model potential energy expressions given above.

The general expression, compared with (11) and (16), for vibrational energy levels within a given electronic state is given by

G{v) - o j ^ i v + y ^ )- co^x^ (y + y^ f + {v + y f + . . . ( 18)

where etc., are additional anharmonic vibrational constants. As with rotational con

(26)

sions for the vibrational constants can be obtained for some o f the model potential energy expressions given above.

The electronic energy o f the ground state relative to atoms at infinite separation is given by -Dg. Alternatively, the minimum o f the ground state PEC can be defined as zero,

Te = 0, and the minimum energy o f other electronic states then made relative to the ground

state. The latter convention is adopted herein.

The total energy o f a given state is the summation o f the rotational, vibrational, and elec tronic components.

G4y)+7; (I!))

Vibrational transitions

With truncation after the second term, the vibrational energy level spacing is given by

AG = G(y)-G(i;-l)

= [®e + + K Y ]~ “ K )“ “ / i f ] (20)

= ry„ - 2 v a > x .

or, commonly referred to as AGuf ■/„

(27)

Figure 2.1 indicates that there are a finite number o f bound vibrational levels. The disso ciation energy, De, is reached when the vibrational spacing becomes zero.* The number of bound vibrational levels, t/max, can be derived by setting dG/dy = 0, resulting in

A). 1

2 (22)

De is determined as the energy of the fmax level:

f CÙ.

(23)

CÙ.

Birge and Sponer developed a graphical method for calculating Dg from AGw-% by plotting AGw-14 versus (t/FlA). The user is able to extrapolate to AG^% = 0 and estimate Umax and

Dg. This method is commonly referred to as a linear Birge-Sponer extrapolation."*^ Non linear behavior at high v is frequently observed with this method, which often results in an overestimate o f Dg. If non-linear behavior is evident, non-linear methods can be used to more accurately estimate Umax and Dg."*®

* An alternate, incorrect, determination o f found in some texts involves assuming Z)g is reached when the vibrational spacing becomes zero. I.e., (20) is set to zero, giving the number o f bound vibrational levels, = coJ{2co^xJ- Substitution o f into (18) returns

+K <y.

4ry.x.

w hich differs from (23) by Although the difference is small, the flaw in the logic is the assumption that there is a vibrational energy level at D^.

Some texts state that is calculated from

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E ffect o f isotope substitution on vibrational energy levels

A change in the mass of one or hoth nuclei, through the addition or removal o f a neutron, does not affect the potential field in which the electrons move.* Thus, the potential energy diagram o f a species is independent o f the isotopic mass o f the nuclei. However, the energy required to move the nuclei within this potential well is dependent on their mass. The harmonic energy, co^ in (11), is dependent on its isotopic mass through the reduced

mass, fi. By changing one or more isotopic masses, we find that changes by a factor p,

the isotopic ratio.

Noting that Dg is independent o f the isotopic mass, we find a relationship between cOe and AigTg through Equations (23) and (24).

.•2

JD, = (o.z: = (25)

The trend shown in (24) and (25) extends to higher order vibrational anharmonic terms as well.'^^ Substitution into (18) leads to the following expression for estimating the position o f isotopically substituted vibronic transitions. The change in the transition energy for vibrational and vibronic transitions, calculated in (27) and (29), is useful for identifying the composition o f a compound and assigning v to the progression.

G' (z/) = + X ) - + X y + A).}", (z/ + + ... (26)

* _{A n electronic isotope effect does exist w hen the y/^ and y/y are not separable (breakdown o f the}

Bom -Oppenheim er approximation). This is most pronounced for bonds to hydrogen, where the electronic shift o f the zero point energy (zpe) is up to 20 cm'*. Coupling o f % and y/y is not lin ear, and an electronic isotope effect is not observed for bonds not involving hydrogen, which is the case herein.'*’

(29)

= [®e (^ + K )“ 'ê-ê + + <ê-ê (^ + X) ] (27) = (l - /))&), + >^) - (l - Z'' K + x y

Vibronic transitions

Transitions between electronic states can readily be addressed as an extension o f the dis cussion o f V ibrational transitions by the addition o f Te to the formulae. Each bound electronic state has a vibrational progression determined by the geometry o f the PES.* Because the vibrational and rotational constants are state dependent: one convention is to ascribe a double-prime (") to constants o f the lower electronic state and a prime (') to con stants o f the upper electronic state.

From (19), the vibronic transition energy can be expressed as

^ E = E ' { v , J = 0 ) - E ' ' { v , J = O)

= { G '{ v )+ T :] -[G " { v y r^

There is no restriction on the change in vibrational quantum number during electronic transitions. The effect o f isotopic substitution on a vibronic transition, assuming no elec tronic isotope effect,^ becomes

= k - K ) - k ' - T " ' ) + A G ' ' " ( y ) - A G " ' " ( y )

= 0 - 0 + [(l - p )(d'^ {v' + y 2 ) - { l- p ^ ) o } X { ^ ' + / i f ] “ [(l “ p ) ^ 'l + K) “ k (^" + / i f ]

= k p ) [ x ( ^ '+ x ) - + x ) ] - (i - + x y - + x y ]

* And each vibrational level has a rotational progression, t See the footnote on page 13.

(30)

For the f'-O transitions, (29) reduces to 25 A E ” (1 - 0 ) = (1 - p ) | |< » ; - 1 < 1 - (l - ^ 4 4 2 c 2 (30)

From (30), it is apparent that the m agnitude o f the shift depends on the isotopic ratio, (24), and on the differences in vibrational quanta and the difference betw een { ry ", ® '} and { cy^x", <y,x^}. In the absence o f a large difference in these param eters, there is no shift in the 0 -0 transition but an increasing shift with increasing Av.

Electronic transitions

The interaction o f a system with electrom agnetic radiation, cf, can be treated as a pertur bation on the system if the radiation is weak. m oderates the interaction o f the external electric (Eo) or m agnetic (Bo) field and the respective m oments, /i,* w ithin the molecule.

(31)

The transition moment, M, betw een initial state m and final state n is defined as

(32)

(31)

and the line strength, S, as the square o f the transition moment.

(33)

Electric moments

Molecules contain a separation o f charge by virtue o f the spatial location o f the electrons and nuclei. An electrical potential, F(r), is established within the molecule. The potential can be expanded as

= F , + F ; z + F ;y + F ;z + ^ + ^ + ...

(34)

With the classical potential energy o f the distribution given by,

E = Y u ^ i V { x .,y .,z ) ₍₃₅₎

A transition between states occurs when there is a resonance between an intramolecular process o f energy E and an external electromagnetic field of energy Eq. Substitution of (34) into (35) gives

/ /■ ; / (36)

The moments o f the charge distribution can be defined from (36) as

zeroth moment (total charge) ₍₃₇₎

M y

\Mz J

i

V i y

(32)

Q

6 . G;=

Q y x Q y y Q y z

G « G z z

Qmn ~ ^J second moment (quadrupole)(39)

I j

In general, the line strength o f each successive moment decreases. However, some situa tions exist where a given moment has zero magnitude because o f symmetry: D„h, Ta, Oh, Ih.

In the Bom-Oppenheimer approximation, each moment can be divided into electronic and nuclear components. For the dipole moment,

M = McUc+Mnuc (40)

Electric dipole transitions

Application of (1) and (40) to (32) and returning to conventional spectroscopic notation results in

s / —I W W // 4-/# \w'' u/" nm \ elec nuc |r^ e le c A^nuc] elec nuc /

(41)

— / u / ' l / y

\w" \lw '

1*/^" \ _ L / y y '

\ii/" \(w '

Orthogonality o f wavefunctions makes the first term zero when considering transitions within a single electronic state and the second term zero when considering transitions between different electronic states. This is the basis for UV/visible (rovibronic) and infra red (rotational and rovibrational) transitions, respectively.

Expansion o f M„m for vibronic transitions results in

= ( K K K K | K K (/J < )

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The translational, rotational, and nuclear overlap integrals are independent o f the PESs and integrate to unity. The resulting line strength, from (33), is

(33)

= | ( K k i e c k é ' ) f I V s k D f l K k v ) f ( 4 3 )

The first term is the electronic transition dipole moment operator, Mg. Mg is dependent on the atomic coordinates o f the nuclei; however, Mg changes slowly and is assumed to be constant in the region bounding *F”. Failure o f this assumption leads to a breakdown o f

the Bom-Oppenheimer approximation since are no longer separable.

The spin overlap integral is unity if the spin is unchanged and zero if the spin changes during the transition. This is valid only if the total spin quantum number, S, commutes with the Hamiltonian (i.e., it is a good quantum number). Inclusion o f additional terms, such as spin-orbit coupling, results in S not commuting with.Æ', and transitions with à S

0 occurring. This is the case with the RhO transitions in question: - ^ZT.

The vibrational overlap integral is non-zero since the vibrational wavefunctions belong to different PESs. Their overlap is highly dependent on the shape o f the PES and the specific vibrational quantum numbers involved in the transition, ranging from zero to unity for

varying combinations. is known as the Franck-Condon factor, and is a domi

nant factor in (43).

Excited state lifetimes

The lifetime, r, o f an excited state provides information about the nature o f the state and on competing relaxation processes. Lifetime measurements, used in conjunction with methods that probe individual state-to-state processes, provide complementary informa tion to validate vibronic assignments.

Spontaneous emission is a unimolecular process. The intensity, 7, follows a single-expo nential profile.

-t

(34)

where /q is the emission intensity at t = 0 and r is the lifetime o f the excited state. If mul tiple processes are occurring on approximately the same timescale (similar lifetimes), the intensity will be the product o f multiple unimolecular processes.

/ ( / ) = / , ( 4 5 )

i

Such processes include emission to multiple states, predissociation, and internal conver sion. The observed lifetime would be

The radiative lifetime, r„™, line strength, S„m, and Einstein spontaneous emission coeffi cient (A coefficient), A„m, are related through (47) for electric dipole transitions (see Ref erence 49 for a broader discussion on this topic).

Lifetime determination

In practice, corrections are made for complications arising from the laser pulse duration and response time of the detection system. The response time approximates a unimolecu lar process and can be accounted for by adding another term with fixed detector- Correction for the laser pulse duration requires that (45) be convoluted by the laser pulse form or the observed signal be deconvoluted accordingly. If the pulse form is assumed to be gaussian, the convolution can be expressed as^^

J m l ' -(‘-t'f ■^4na h ■yjAna dr' |c c 0 zL ₀ -e ^ erfc I ^

048)

(35)

where a is the standard deviation o f the laser pulse and erfc is the complementary error function defined by

erfc(x) = l - e r f ( x ) = - ^ [e"'‘ dv (49)

(36)

3 . E

x p e r i m e n t a l

S

e t u p

Laser ablation has become a standard method o f rapidly converting detectable quantities of a solid to the gas phase. From metals to proteins, solids have been prepared for analy sis, quantification, or further reaction. Fundamental researeh has adopted this technology to prepare metal clusters and metal compounds. In this laboratory, a Nd:YAG laser vaporized rhodium metal, ereating a metal plume into a pulsed molecular beam that con tained one or more reactive gases. The reactant gas(es) was activated (dissociated) by the laser and ablated metal. Reaction occurred as the carrier gas transported the metal vapor and reactant gases through a channel. In the channel, the metal vapor thermalized with the gas, to around room temperature, and reacted to form metal clusters and compounds. The carrier gas and reaction mixture further cooled during an unskimmed supersonic expan sion into a high vacuum chamber. Translation carried the reaction mixture into the analy sis region. A second Nd:YAG laser pumped a tunable dye laser to excite rovibronic tran sitions in the species present. Emission from the laser-excited compounds was collected, filtered with a monochromator, and detected on a photomultiplier tube (PMT). The signal was digitized on a digital storage oscilloscope and transferred to a computer for storage and post-processing. Figure 3.1 schematically shows the experimental setup used in this laboratory. Each component is detailed below.

Experimental components

Pulsed molecular beam source

The reactant gas mixture was prepared by diluting '^02 (PraxAir, 99.9 %) and/or '^0% (Cambridge Isotope Labs., 98 %) with sufficient helium (PraxAir, 99.9995 %) to prepare an approximately five percent mixture in a ten liter glass bulb. The pressure inside the bulb was initially 1.5 to 2.0 atm. and used until the pressure dropped below I.O atm. Tef lon tubing carried the gas to the nozzle.

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Gas Inlet

] Pulsed

j Nozzle Rhodium » Rod & Stagl Ablation Laser D ye L a s e r Probe Laser 96 % T S ig n a l C o lle c tio n Top View) Side View OGE C alib.

Nozzle & Rod

(se e S ide View) Ablation and Probe Lasers Top View « ^

n

[ L

Digital D elay G e n e ra to r Dye L a s e r C o n tro lle r C o m p u te r T im ing C a rd PMT Digital S to r a g e O s cillo sc o p e C o m p u te r

Figure 3.1 Experimental setup for collection o f LIE and DF. The optogalvanic cali bration experiment is discussed on page 55.

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The nozzle follows a standard design by Proch and Trickl.^' It consisted o f a valve stem mounted to the center o f a piezoelectric disk (Physik Instrument, P286.20). The gas mix ture is contained in the volume surrounding the piezoelectric disk and valve stem. The valve stem covers a 0.5 mm orifice joining the interior o f the nozzle and the high vacuum chamber. The piezo crystal was triggered by the computer, which activated a pulsed vari able voltage (0 to 1 000 VDC), variable duration (0 to 700 ps), and variable delay (0 to 360 ps) circuit. The valve stem was adjusted to keep the voltage required to lift it below 400 volts, which increased the longevity of the crystal. A trade-off exists between the vol ume o f gas and the background pressure in the vacuum chamber and the load on the diffu sion pump. Importantly, more gas does not mean greater signal since the amount o f metal ablated is the limiting factor. The background pressure controls the degree o f cooling during expansion; pumping speed was controlled to obtain spectra at increased tempera tures. The pulse duration was nominally 350 ps and optimized by monitoring the LIF sig nal. The delay was always zero since it could be centrally controlled from the computer. Below the nozzle was mounted the laser ablation assembly.

Laser ablation assembly

Three mutually perpendicular holes allow for the intersection o f the reactant gas stream, metal rod, and ablation laser beam (see the Side View o f the vacuum chamber in Figure 3.1). Perpendicular to the nozzle orifice was a 2.0 mm channel that directed the expanding gases past the rhodium rod. The channel length beyond the rod was variable, allowing for different residence/reaction times between the gas and metal after ablation. A 17 mm channel was used to generate RhO since it was observed that the yield o f RhO depended on the length o f the channel beyond the ablation region. The 17 mm channel had gener ated high yields o f RhO during previous experiments in our laboratory. The rotating and translating rhodium rod (5.0 mm diameter x 30.0 mm; 99.9 % purity; Goodfellow) was mounted perpendicular to the gas channel. The rod was 2.5 mm off-axis to allow the gas to pass unimpeded past the rod, and simultaneously rotated and translated by a stepping motor operating at between 15 and 20 Hz. The motor was mounted inside the vacuum chamber. The second harmonic (532 nm) o f a Continuum NY61 Nd:YAG was focussed onto the surface of the rod by a convex lens (50 cm focal length). Between 50 and 100 mJ/pulse and a nominal pulse duration o f 8 ns ablated the metal rod and created a plasma

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in the local carrier gas volume. The laser was timed to coincide with approximately the center o f the carrier gas volume. The surrounding carrier gas swept the plasma into the reaction channel, allowing for continued reaction and thermalization o f the plasma. The products cooled during a supersonic expansion into the high vacuum chamber. Both laser power and timing were optimized for maximum product yield. The optimum laser power was below the maximum o f the laser; with maximum power, the plasma did not quench in the reaction channel and was observable in emission immediately after expansion. No spectra could be recorded under these conditions.

The high vacuum chamber consisted o f a 30x30x30 cm^ cubic aluminum housing, pumped by an Edwards Diffstack 160 diffusion pump and an Edwards E2M8 mechanical backing pump. Pressure inside the chamber was monitored with a Granville-Phillips 270006 ion gauge. The background pressure was typically 10'® Torr (1 Torr = 1 mmHg = 1/760 atm.). In operation, the pressure increased by a factor o f 10 to 100, depending on the molecular beam volume. The nozzle, optical ports, and collection optics were mounted to other faces o f the vacuum chamber as shown in Figure 3.1.

Detection & data collection

A Lumonics YM600 Nd:YAG laser operating at 355 nm pumped a Lumonics HD-300 tunable dye laser (probe laser), which intersected the supersonic molecular beam perpen dicularly. This laser was timed to probe the products created in the ablation mixture as they passed through the optical path of the emission detection system. The region from 380 to 700 nm was scanned using a series o f laser dyes (Exciton Inc.: Exalite 389, 398, 404, 416, and 428; ED 390; Stilbene 420; Coumarin 440, 450, 460, 480, and 485; Rho- damine 590, 610, and 640; Kiton Red 620; and DCM). Emission was collected perpen dicular to both beams by two 5.0 cm diameter x 7.5 cm focal length lenses and imaged onto the entrance o f a Jobin-Yvon H20 monochromator. A Hamamatsu R1477 photomul tiplier converted the photon intensity to an electrical signal. (See Appendix B for a discus sion o f the optical setup.)

The signal was digitized with a Tektronics 2440 digital storage oscilloscope and trans ferred to a personal computer. The computer was equipped with a GPIB board and an

(40)

Advantech PCL-830 timer card. In-house software controlled the system timing and data collection. Detailed timing sequences are shown in Figure 3.2 and 3.3. The digitized sig nal is the emission decay profile (Figure 4.4 on page 47). Software processing allowed for user-selectable region(s) o f the decay profile to be extracted and plotted against alterna tive axes, such as dye laser wavelength, pump laser wavelength, or time. The dye laser wavelength was corrected as described in Appendix C.

Typical instrument settings are given in Appendix D.

Experimental details

Laser-induced fluorescence*'^

LIF provides information on rovibrational energy levels o f the molecular ground and excited states. LIF records emission as a function o f probe laser wavelength. Demtroder^^ and Andrews^^ have summarized some o f the standard LIF techniques as well as recent developments. In our experiments, the monochromator usually passed the zeroth order (all emission) but was sometimes set to detect emission to an excited ground state vibrational level to filter overlapping electronic bands (wavelength filtering). With a fully open aperture, the monochromator bandpass was % 100 cm"' in the visible region, sufficiently wide to encompass an entire RhO band. Alternatively, for bands with different excited state lifetimes, different regions o f the emission decay could be recorded and mathemati cally scaled to isolate individual bands (lifetime filtering).^"*

For a given laser dye, a low-resolution scan over the entire dye curve identified the bands in that region. Individual bands were subsequently scanned at higher resolution, typically 0.001 nm, with five to fifteen laser shots averaged per wavelength. Optogalvanic spec troscopy o f an iron-neon hollow cathode lamp was used to fine-tune the probe dye laser’s internal calibration (see Appendix C).

* The terms ‘laser-induced fluorescence’ and ‘dispersed fluorescence’ are standard in the science and will be used herein, however, the reader should note that the transition in question has been shown to be spin-forbidden in nature, i.e., phosphorescence.

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Computer Controlled Timer Board

(1 ps resolution)

C h a n n e l (all tim es in m icroseconds ) _{E v e n t} _{N o t e s}

1 2 3 4 5 6 7 8 9 10 1000 850 740

IF

750

IF

550 J h . 1002 10 EG&G Trigger

Lumonics Flashlam p Optimum: 180 g s before Q-switch Infinity F lashiam p Optimum: 260 p s before Q-switch

Continuum Flashiam p Optimum: 250 p s before Q-switch at 11 m s C om puter Trigger 500 p s duration

N ozzie Zero deiay on HV box. 1 0 0 PMT G ate » 2 ps after Lumonics Q-switch

Continuum +5 V Required for externai trigger (-1 ; 5000; 2)

Figure 3.2 Timing signals for the computer timing card. Time zero is the left vertical dashed line with time increasing to the right. The right vertical dashed line corresponds to the rising edge o f the timing pulse sent to the digital delay gen erator (see Figure 3.3). The delay, duration, and pulse direction are indicated. All voltage pulses are 5 V. Some tim ing signals were not used in the experiments but are included for completeness.

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EG&G Digital Delay Generator

(0.01 ns resolution) C h a n n e l (all tim es in n a n o s e c o n d s ) _{E v e n t} _{N o t e s} To + 5 V not used A +5 V 1000 1___________ see AB B +5 V 300 1 1000 see A 3 C D + 5 V +10 V not used

betw een (25000 an d 65000) n s Lum onics Q-switch & T he probe ia s e r an d th e sc o p e are triggered together. T h e se d elay s a cco u n t for th e flight tim e of

A -B +5 V 300

_J

Continuum Q-switch probe region (Lumonics).

C -D + 5 V not used

Trigger on the forward edge; the trailing edge is a slow exponential decay.

Figure 3.3 Timing signals for the digital delay generator. The left vertical dashed line is time zero supplied by the computer tim ing card (see Figure 3.2). The delay, duration, magnitude, and pulse direction are indicated.

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Dispersed fluorescence*

DF provides information on the vibrational levels in the ground state and on other low- lying electronic states. Whereas LIF considers the total emission intensity, DF considers the wavelength(s) at which emission is occurring. The DF intensity depends on the over lap of the vibrational wavefunctions (Franck-Condon factor), (43). In this setup, the probe laser was tuned to a strong rovibronic transition and then the monochromator scanned from above the probe laser wavelength to longer wavelengths. This allows for the detec tion of hot transitions and provides an internal calibration. A secondary calibration was obtained by allowing the monochromator to scan to sufficiently long wavelengths that second order dispersion was observed. Five to fifteen probe laser shots were averaged per monochromator step. A 0.5 mm aperture yielded a bandpass o f » 20 cm'^ and was a com promise between signal and resolution. The precision o f the band center was ± 2 cm'^ and found by fitting the band to a gaussian function, which determined the mass-weighted band center irrespective o f the actual profile. We estimate the accuracy o f the DF spectral intervals to be ± 15 cm '.

Excited state lifetimes^

Intensity-decay profiles were obtained by tuning the probe laser to a rovibronic transition and then recording the unaltered decay profile (intensity vs. time). Up to 500 probe laser shots were averaged for each transition. Typically, three to five lifetime measurements were averaged to give a band-averaged lifetime. The precision o f a typical profile was ± 5 ns whereas the precision o f the band-averaged lifetime was ± 100 ns (taken as the stan dard deviation o f the individual measurements).

t LIF, DF, and lifetime experiments were conducted separately. It is possible to design an experi ment where all three are recorded simultaneously using a streak camera. A part from the initial expense (200 000 USD), such a system would allow for rapid data collection and provide more versatility for data processing. Large data-storage capabilities would be required; a single image w ould represent excitation at a single probe laser wavelength and could be 10 MB; thousands o f images would comprise a single band.